The Swiss fourth seed wore down the veteran Stepanek 6-2, 6-3, 6-4 in just over two hours on Hisense Arena and will face another Czech Lukas Rosol in the round of 32.
Wawrinka's win over the 37-year-old, who had to qualify for this year's main draw, stretched his winning streak over Czech players to 11 and he has the chance to make that 12 against Rosol on Saturday.
He has not lost to a Czech player since he was defeated by Tomas Berdych in the Davis Cup first round in 2013.
"I'm confident with my game. I know it depends a lot of me when I go into the match against many players. Trying to be as focused as I can," Wawrinka said.
Wawrinka beat Novak Djokovic and Rafael Nadal on the way to winning the 2014 Australian Open.